A hyperbolic free boundary problem modeling tumor growth: Asymptotic behavior
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Publisher:American Mathematical Society
Citation:Xinfu Chen, Shangbin Cui and Avner Friedman, "A hyperbolic free boundary problem modeling tumor growth: Asymptotic behavior," Transactions of the American Mathematical Society 357, no. 12 (2005), doi:10.1090/S0002-9947-05-03784-0
In this paper we study a free boundary problem modeling the growth of radially symmetric tumors with two populations of cells: proliferating cells and quiescent cells. The densities of these cells satisfy a system of nonlinear first order hyperbolic equations in the tumor, and the tumor's surface is a free boundary r = R(t). The nutrient concentration satisfies a diffusion equation, and R( t) satisfies an integro-differential equation. It is known that this problem has a unique stationary solution with R( t) = R-s. We prove that ( i) if lim(T-->infinity) integral(T+1)(T)\(r) over dot(t)\dt = 0, then lim(t-->infinity)R(t) = R-s, and ( ii) the stationary solution is linearly asymptotically stable.
First published in Transactions of the American Mathematical Society in volume 357, issue 12, published by the American Mathematical Society.
Rights:Copyright 2005, American Mathematical Society
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